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Binary extended perfect codes of length 16 and rank 14

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Abstract

All extended binary perfect (16, 4, 211) codes of rank 14 over the field F 2 are classified. It is proved that among all nonequivalent extended binary perfect (16, 4, 211) codes there are exactly 1719 nonequivalent codes of rank 14 over F 2. Among these codes there are 844 codes classified by Phelps (Solov’eva-Phelps codes) and 875 other codes obtained by the construction of Etzion-Vardy and by a new general doubling construction, presented in the paper. Thus, the only open question in the classification of extended binary perfect (16,4,211) codes is that on such codes of rank 15 over F 2.

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Authors and Affiliations

  1. Institute for Information Transmission Problems, Moscow, Russia

    V. A. Zinoviev & D. V. Zinoviev

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  1. V. A. Zinoviev
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  2. D. V. Zinoviev
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Original Russian Text © V.A. Zinoviev, D.V. Zinoviev, 2006, published in Problemy Peredachi Informatsii, 2006, Vol. 42, No. 2, pp. 63–80.

Supported in part by the Russian Foundation for Basic Research, project no. 06-01-00226.

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Zinoviev, V.A., Zinoviev, D.V. Binary extended perfect codes of length 16 and rank 14. Probl Inf Transm 42, 123–138 (2006). https://doi.org/10.1134/S0032946006020062

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  • DOI: https://doi.org/10.1134/S0032946006020062

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